Answer:
37.7
Step-by-step explanation:
<h2><u>circumference of a circle:</u></h2>
Formula = 2πr
r is the radius
diameter = 2* radius
hence radius = 12/2
radius = 6 yards
2*π*6 = 37.6991
to 3sf
<h3><u>circle circumference is 37.7</u></h3>
Answer:
B. $200,000
Step-by-step explanation:
Let x be the amount placed at 5.5%
3x is the amount placed at 5%
This leaves the rest for the 4.5 % 500000- x - 3x = 500000-4x
Assuming simple interest
I = PRT where I is interest, P is principle, rate is rate and t is time
Interest for the 5.5% for 1 year is
I = x * .055 * 1 = .055x
Interest for the 5.% for 1 year is
I = 3x * .05 * 1 = .15x
Interest for the 4.5% for 1 year is
I = 500000-4x * .045 * 1 = 22500 - 0.18 x
Add the interest together to get the income for 1 year
.055x+ .15x+22500 - 0.18 x=25,000
Combine like terms
0.025x+22500=25000
Subtract 22500
.025x =2500
Divide by .025
x =100000
short term notes is 100000
3*x = 300000 = government bonds
The rest is utility bonds 500000- 100000-300000 = 100000
We want how much more in government bond than utility bond
300000 -100000 = 200000
Part A. The correlation coefficient, denotes as R^2, is a measure of how well does the data point correlate with a given model or equation. The closer the R^2 is to 1, the better is the correlation. However, R2=1 is ideal for scatter plots. Using the MS Excel to execute the regression, the data points was fitted to a quadratic equation. The R2=0.9983. From the choices, the closest answer would be 1. But as stated previously, a value of 1 is ideal only. Therefore, the answer is most likely 0.94,
Part B. To determine the slope, the equation would be Δy/Δx. For x=5 and x=10, the slope would be
Slope = (3-1)/(10-5) = 2/5 or 0.4. This is the instantaneous rate of change at the interval of 5 to 10 days.
Part C. The difference between causation and correlation is identifiable if you know the direct relationship between the variables. In this case, the increase in radius is not caused by time. The problem does not state so. But we know from the trend shown on a graph, that there is a correlation between these variables. Therefore, the answer is correlation.
<span>Amplitude: 3; period: pi/2; midline: y = 2</span>
Given that the vertex (h, k) is (5, 2), you know the vertex form will look like
f(x) = a(x -5)² +2
for some value of "a" that makes f(4) = -3. That value of "a" can be found by substituting the given values in the above equation for f(x) and solving for "a".
-3 = a(4 -5)² +2
-3 -2 = a×1²
a = -5
This means the appropriate choice is ...
C) Vertex form: f(x) = -5(x -5)² +2; Standard form: -5x² +50x -123